Let's take a look at two of the cards:
"Ugh ugh" - I'd love to know who it was that first put down "ugh ugh" as words or speech of Native people!
The headdress itself - One of the common stereotypical ways that a headdress is drawn.
The geometric trim around the heart - I guess this could be traced to textiles Native artists weave on looms. But don't artists from other groups also use looms in creating their woven items?
Wondering about his "give me" line. What do you think about that?
And or course, he is playing Indian. The artist didn't intend you to think the boy is actually Native. That's different (mostly) from the other Valentine's Day cards in the BuzzFeed article...
Here's the second one:
"How" - Another utterance someone attributed as the way that Indians say hello. You remember it from Disney's Peter Pan?
The headdress - Another of the common ways that a headdress is drawn...
Given her skin tone, we can speculate that the artist meant her to actually be Native, but that's not likely. Like the boy in the card above, she's most likely playing Indian, too.
If you want to see more, check out the ones Adrienne K. has been posting each year at Native Appropriations. As far as I know, makers of the Valentine's day cards no longer use these stereotypes. I wish authors and illustrators of children's and young adult literature would stop, too!